Geodesic
“Quantization" of an isomonodromic Hamiltonian Garnier system with two degrees of freedom
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 39-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct solutions of analogues of a time-dependent Schrödinger equation corresponding to an isomonodromic polynomial Hamiltonian of a Garnier system with two degrees of freedom. The solutions are determined by solutions of linear differential equations whose compatibility condition is the given Garnier system. With explicit substitutions, these solutions reduce to solutions of the Belavin–Polyakov–Zamolodchikov equations with four times and two spatial variables.
Keywords: Schrödinger equation, Hamiltonian, Belavin–Polyakov–Zamolodchikov equation
Mots-clés : isomonodromic deformation, Garnier system, Painlevé equation. 
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D. P. Novikov; B. I. Suleimanov. “Quantization" of an isomonodromic Hamiltonian Garnier system with two degrees of freedom. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 39-57. http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a3/

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